Make sure that your tractor performs all the basic tasks properly, so check the steering, gears, forward and reverse, PTO, lift, lights, indicators and hydraulics. Even if you wish to work on it right away, you probably won't be interested in a complete refurbishment for some time and need to minimize the number of initial jobs. You should have a detailed check list which included at a minimum the following: does it start easily from cold, run well when hot, all the electrical components work well, does it have good traction If possible you should go to your test armed with a toolbox containing a compression tester, expensive Fluke digital multimeter, hydrometer, and other specialty tools. or bring somebody with you who has these tools.. If you are not lucky enough to have access to these tools, as many don't then don't panic. You should in this case rely on your own common sense and your own observation skills.
Does it start easily from cold? - A tractor that starts easily will eliminate several particular problems in one shot Good Battery, compression, ignition wiring / magneto, tune up, fuel flow, Carburetor can be assured (not guaranteed) by this. If it doesn't start easily, it still may be a good machine but you will have to spend some time and money on it. One thing you should be watch out for is if the tractor is out and warmed up when you arrived, you lose an important checklist item, namely the cold start, because as we all know a warm engine starts much more easily then a cold one..
How does it run when warm - Make sure you get it hot, as you will want to ensure it doesn't overheat. There a number of problems to watch out for that can cause the tractor to run poorly after it warms up. Plan on spending a half-hour running it. Look for leaks, both oil and antifreeze. Then, shut it down and see how it starts up again.
Do the brakes work well - Although inexpensive to replace, they are inaccessible on many tractors and will require extensive teardown to get the new ones in.
Does it generate a lot of - Blue smoke indicates many potentially difficult problems like rings, pistons, or valve guides. White or black smoke can frequently be corrected with carburetion or ignition changes but still involves your time and also money.
Does it make clunking noises from inside the engine - A simple ticking from the top of the engine may be a simple valve adjustment but a deep thunk from the bottom or middle of the engine would show very serious and expensive repairs. The clunk should be more pronounced under load. This may be an indication of trouble with the piston, bearings or crankshaft rods. And mean a very expensive repair job.
Use the hydraulics - Check the full range of the power rams by extending them with a load. Let the load stand in the hold situation for a period to be sure that there is no leakdown. Chattering noises from the pump while lifting suggest the pump is not getting enough supply of hydraulic oil. The pump might have experienced a lot of wear when run this way for long periods of time and may be ready to fail.
While many of the above experiences may sound a bit negative, you should do your research and understand the particular issues the model of tractor you are looking at before you invest.